Heterogeneous catalysis plays a key role in the manufacture of essential products in key areas of agriculture and pharmaceuticals, but also in the production of polymers and numerous essential materials. Our understanding of heterogeneous catalysts is advancing rapidly, especially by using the latest characterisation methods on these relatively complex effect materials. At the heart of these catalytic processes, both selective oxidation and hydrogenation play a key role. Both oxidation and hydrogenation exhibit similar requirements since often a partial reaction product is required, rather than the products of total hydrogenation or oxidation, in the latter case this being typically carbon dioxide and water. This Feature Article considers the approaches available for catalyst discovery and design for heterogeneous catalysts. Three catalysts are considered in detail, two exemplifying oxidation and the other selective hydrogenation. The design of vanadium phosphates for the selective oxidation of butane to maleic anhydride is described in terms of the search for advanced materials with superior activity. This is achieved through the synthesis of wholly amorphous vanadium phosphates. The design of supported gold and gold palladium alloy catalysts for the oxidation of carbon monoxide and the direct hydrogenation of oxygen to form hydrogen peroxide is described and the problems concerning selectivity control are discussed.